Uniform Minor-Arc Cancellation for Primes at the X^{2/15+ε} Scale
We prove uniform cancellation in prime-weighted exponential sums at the 2/15 scale, improving the 8/33 local Fourier scale in the Matomäki–Radziwiłł–Tao machinery for averaged prime-pair correlations. On the minor-arc part of every centered arc of radius 1/(2H), the squared von Mangoldt exponential sum over X 0 and epsilon > 0, once H >= X^(2/15+epsilon) and X is large enough. The center may lie anywhere on the circle. The same cutoffs and constants work for every center and are chosen before X and H. This gives uniform minor-arc cancellation at the 2/15 threshold. Since 2/15 < 8/33, the…
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